Facilitating productive mathematical argumentation, especially asking rational questions, is essential yet remains challenging for pre-service mathematics teachers (PMTs), who often have limited opportunities to apply abstract theoretical knowledge in authentic practice. At the same time, recent advances in large language models (LLMs) have expanded the potential for simulating students in educational settings, enabling low-risk environments for instructional practice. To inform the design of a system that supports PMTs in orchestrating classroom argumentation, we conducted a formative study with eight experienced mathematics teachers to identify key design requirements, including personalization, realistic simulations, structured reflection, and ease of use. Building on these requirements, we developed ArguMath, an AI-simulated classroom environment that supports PMTs in practicing the orchestration of mathematical argumentation. ArguMath comprises three core components: (1) customization of classroom settings; (2) simulation of classroom discussions with AI-based students grounded in authentic transcripts and augmented with real-time instructional suggestions; and (3) structured reflection through discourse annotation and overall feedback. Results from an exploratory user study with seven PMTs, complemented by interviews with four experienced teachers, indicate that ArguMath has the potential to support PMTs' classroom orchestration skills, particularly theory-aligned questioning strategies.

翻译：促进富有成效的数学论证，尤其是提出合理性问题的能力，对于职前数学教师至关重要却又极具挑战性——他们通常缺乏在真实教学情境中应用抽象理论知识的机会。同时，大型语言模型的最新进展拓展了教育场景中学生模拟的潜力，为教学实践提供了低风险环境。为设计支持职前教师组织课堂论证的系统，我们面向八位资深数学教师开展形成性研究，明确了个性化、真实模拟、结构化反思和易用性等关键设计需求。基于这些需求，我们开发了ArguMath——一个辅助职前教师练习数学论证组织技能的人工智能模拟课堂环境。ArguMath包含三大核心模块：(1)课堂情境自定义设置；(2)基于真实教学转录文本、结合AI实时教学建议驱动的学生课堂讨论模拟；(3)通过话语标注与综合反馈实现的结构化反思。面向七位职前教师的探索性用户研究结果，辅以四位资深教师的访谈表明，ArguMath具备支持职前教师课堂组织能力的潜力，尤其在符合理论导向的提问策略方面效果显著。